Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x + 2$ and $ BC = 4x + 18$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x + 2} = {4x + 18}$ Solve for $x$ $ 4x = 16$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({4}) + 2$ $ BC = 4({4}) + 18$ $ AB = 32 + 2$ $ BC = 16 + 18$ $ AB = 34$ $ BC = 34$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {34} + {34}$ $ AC = 68$